Effect of the wheel/rail kinematic variables and geometry on the dynamics of railroad vehicles

The first objective of this work is to present general computer formulations for the wheel/rail contact problem. Four nonlinear dynamic formulations for the analysis of the wheel/rail contact are presented, compared and their performance is evaluated. Two of these formulations employ nonlinear algebraic kinematic constraint equations to describe the contact between the wheel and the rail (constraint approach), while in the other two formulations the contact force is modeled using a compliant force element (elastic approach).; The second objective is to study the effect of linearization of the kinematic equations on the vehicle dynamics. The sensitivity of the wheel/rail contact problem to the approximations made in some of the creepage expressions is examined. It is known that railroad vehicle models that employ kinematic linearization can predict, particularly at high speeds, significantly different dynamic response as compared to models that are based on fully nonlinear kinematic and dynamic equations. The velocity creepage expressions that result from the use of the assumptions of small angles are obtained and compared with the fully nonlinear expressions. Newton-Euler equations for the wheel set are presented and their dependence on the Euler angles and their time derivatives is discussed. The effect of the linearization assumptions on the form of Newton-Euler equations is examined.; The third objective of this work is to study the effect of wheel profile on the dynamic behavior of the vehicle. The effect of the geometry of a wheel profile that allows only a single point of contact between the wheel and the rail is investigated. The local geometric properties of this profile are compared with the local geometric properties of a profile that allows for two-point contacts in order to understand the basic differences between the two profiles. A simple model is first used to examine the effect of the profile geometry on the stability and nonlinear dynamics of a suspended wheel set. The results obtained show that the wheel profile can significantly alter the critical speed. Using surface parameters that define the wheel and rail geometry, the global representations of the positions of the points on the wheel and rail surfaces are obtained and used to define the conditions of the contact between the wheel and the rail.